Weight polytopes and saturation of Demazure characters

Abstract

Demazure modules are certain B-submodules of highest weight irreducible G-modules, for B a Borel subgroup of a semisimple Lie group G. Their characters are given by the Demazure character formula which, while straightforward to implement computationally, does not make immediately obvious which weights appear in the character. In this talk, we will first consider combinatorial incarnations of these characters--the key polynomials--and their Newton polytopes, recalling work of Monical--Tokcan--Yong and Fink--Meszaros--St. Dizier. We then situate this combinatorial perspective in a broader representation-theoretic framework by introducing weight polytopes of Demazure modules, and show how these polytopes shed light on the support of Demazure characters. 

Zoom link: https://unsw.zoom.us/j/83492167515

(password: 460738)

School Seminar Series: 

• Pure Maths Seminar